import pandas as pd
import numpy as np
from itertools import product

from tqdm import tqdm 

import matplotlib.pyplot as plt
import seaborn as sns

from utils import *

import warnings
warnings.filterwarnings('ignore')

%matplotlib inline

data = pd.read_csv('vodafone_data.csv')

data.head()

	Date	Open	High	Low	Close	Volume
0	2016-02-11	29.330000	29.510000	29.030001	29.270000	4805000
1	2016-02-12	29.520000	29.950001	29.410000	29.900000	3116500
2	2016-02-16	29.950001	30.420000	29.900000	30.260000	4037900
3	2016-02-17	31.000000	31.320000	30.900000	31.090000	4313800
4	2016-02-18	31.090000	31.150000	30.920000	30.959999	3522800

Експлоративний аналіз даних

data['Date'] = pd.to_datetime(data['Date']).dt.date
data['Date_index'] = pd.DatetimeIndex(data.Date)

data['year'] = pd.to_datetime(data['Date']).dt.year
data['quarter'] = pd.to_datetime(data['Date']).dt.quarter
data['month'] = pd.to_datetime(data['Date']).dt.month

data.Date.agg({min, max})

min    2016-02-11
max    2021-02-11
Name: Date, dtype: object

data.shape

(1260, 10)

Розподіл значень ряду по роках

Розподіл кількості значень ряду по роках

data.year.value_counts().plot(kind='bar', rot='45');
plt.title('Qty of observations for each year');

data.year.value_counts(normalize=True).plot(kind='bar', rot='45');
plt.title('Percentage of observations for each year');

Бачимо, що значення часового ряду розподілені практично рівномірно по роках

Розподіл значень ряду

sns.kdeplot(data.Close);

fig, axs = plt.subplots(nrows=data.year.nunique(), ncols=1, figsize=(9, 35))

for idx, year in enumerate(data.year.unique()):
    sns.kdeplot(data.loc[data.year == year, 'Close'], ax=axs[idx]);
    axs[idx].set_title('Distplot for {}'.format(year));

Розподіл значень по роках дає певні "натяки" на наявність негативного тренду

Аналіз пропущених значень

missing_dates = pd.date_range(start='2016-02-11', end='2021-02-11', freq='D').difference(data.Date)

# we have 568 missing dates
missing_dates.nunique()

568

missing_dates

DatetimeIndex(['2016-02-13', '2016-02-14', '2016-02-15', '2016-02-20',
               '2016-02-21', '2016-02-27', '2016-02-28', '2016-03-05',
               '2016-03-06', '2016-03-12',
               ...
               '2021-01-10', '2021-01-16', '2021-01-17', '2021-01-18',
               '2021-01-23', '2021-01-24', '2021-01-30', '2021-01-31',
               '2021-02-06', '2021-02-07'],
              dtype='datetime64[ns]', length=568, freq=None)

missing_dates = pd.DataFrame(missing_dates, columns=['date'])
missing_dates['year'] = missing_dates['date'].dt.year

missing_dates.groupby('year').date.count().plot(kind='bar', rot='45');
plt.title('Qty missing values for each year');

missing_dates.year.value_counts(normalize=True).plot(kind='bar', rot='45');
plt.title('Percentage of missing values for each year');

missing_dates['month'] = missing_dates['date'].dt.month
missing_dates['day'] = missing_dates['date'].dt.day

missing_dates.head()

	date	year	month	day
0	2016-02-13	2016	2	13
1	2016-02-14	2016	2	14
2	2016-02-15	2016	2	15
3	2016-02-20	2016	2	20
4	2016-02-21	2016	2	21

missing_dates.day.value_counts(normalize=True).head()

25    0.040493
4     0.038732
1     0.036972
2     0.035211
3     0.035211
Name: day, dtype: float64

missing_dates.month.value_counts(normalize=True).head()

1     0.093310
12    0.091549
7     0.088028
9     0.086268
5     0.084507
Name: month, dtype: float64

Лінійна інтерполяція для обробки пропущених значень

data.head()

	Date	Open	High	Low	Close	Volume	Date_index	year	quarter	month
0	2016-02-11	29.330000	29.510000	29.030001	29.270000	4805000	2016-02-11	2016	1	2
1	2016-02-12	29.520000	29.950001	29.410000	29.900000	3116500	2016-02-12	2016	1	2
2	2016-02-16	29.950001	30.420000	29.900000	30.260000	4037900	2016-02-16	2016	1	2
3	2016-02-17	31.000000	31.320000	30.900000	31.090000	4313800	2016-02-17	2016	1	2
4	2016-02-18	31.090000	31.150000	30.920000	30.959999	3522800	2016-02-18	2016	1	2

data_no_missing = data.copy(deep=True)

data_no_missing.head()

	Date	Open	High	Low	Close	Volume	Date_index	year	quarter	month
0	2016-02-11	29.330000	29.510000	29.030001	29.270000	4805000	2016-02-11	2016	1	2
1	2016-02-12	29.520000	29.950001	29.410000	29.900000	3116500	2016-02-12	2016	1	2
2	2016-02-16	29.950001	30.420000	29.900000	30.260000	4037900	2016-02-16	2016	1	2
3	2016-02-17	31.000000	31.320000	30.900000	31.090000	4313800	2016-02-17	2016	1	2
4	2016-02-18	31.090000	31.150000	30.920000	30.959999	3522800	2016-02-18	2016	1	2

data_no_missing = data_no_missing.set_index('Date_index').asfreq('D')

data_no_missing.head()

	Date	Open	High	Low	Close	Volume	year	quarter	month
Date_index
2016-02-11	2016-02-11	29.33	29.510000	29.030001	29.27	4805000.0	2016.0	1.0	2.0
2016-02-12	2016-02-12	29.52	29.950001	29.410000	29.90	3116500.0	2016.0	1.0	2.0
2016-02-13	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2016-02-14	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2016-02-15	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

for col in ['Open', 'High', 'Low', 'Close', 'Volume']:
    data_no_missing[col] = data_no_missing[col].interpolate()

data_no_missing.head()

	Date	Open	High	Low	Close	Volume	year	quarter	month
Date_index
2016-02-11	2016-02-11	29.330000	29.510000	29.030001	29.27	4805000.0	2016.0	1.0	2.0
2016-02-12	2016-02-12	29.520000	29.950001	29.410000	29.90	3116500.0	2016.0	1.0	2.0
2016-02-13	NaN	29.627500	30.067501	29.532500	29.99	3346850.0	NaN	NaN	NaN
2016-02-14	NaN	29.735000	30.185001	29.655000	30.08	3577200.0	NaN	NaN	NaN
2016-02-15	NaN	29.842501	30.302500	29.777500	30.17	3807550.0	NaN	NaN	NaN

data_no_missing = data_no_missing.reset_index(drop=False)

data_no_missing.head(3)

	Date_index	Date	Open	High	Low	Close	Volume	year	quarter	month
0	2016-02-11	2016-02-11	29.3300	29.510000	29.030001	29.27	4805000.0	2016.0	1.0	2.0
1	2016-02-12	2016-02-12	29.5200	29.950001	29.410000	29.90	3116500.0	2016.0	1.0	2.0
2	2016-02-13	NaN	29.6275	30.067501	29.532500	29.99	3346850.0	NaN	NaN	NaN

data_no_missing['Date'] = pd.to_datetime(data_no_missing['Date_index']).dt.date
data_no_missing['year'] = pd.to_datetime(data_no_missing['Date']).dt.year
data_no_missing['quarter'] = pd.to_datetime(data_no_missing['Date']).dt.quarter
data_no_missing['month'] = pd.to_datetime(data_no_missing['Date']).dt.month

data_no_missing.head()

	Date_index	Date	Open	High	Low	Close	Volume	year	quarter	month
0	2016-02-11	2016-02-11	29.330000	29.510000	29.030001	29.27	4805000.0	2016	1	2
1	2016-02-12	2016-02-12	29.520000	29.950001	29.410000	29.90	3116500.0	2016	1	2
2	2016-02-13	2016-02-13	29.627500	30.067501	29.532500	29.99	3346850.0	2016	1	2
3	2016-02-14	2016-02-14	29.735000	30.185001	29.655000	30.08	3577200.0	2016	1	2
4	2016-02-15	2016-02-15	29.842501	30.302500	29.777500	30.17	3807550.0	2016	1	2

Аналіз наявності викидів в даних

fig = plt.figure(figsize=(10, 8))
sns.boxplot(data=data_no_missing, x=data_no_missing.year, y='Close');
plt.title('Box-Plots for each year');

Бачимо, що часовий ряд є досить "чистим", також проглядається негативний тренд

Аналіз наявності тренду, сезонності, циклічності

Візуалізація часового ряду

data_no_missing.set_index('Date').Close.plot(title='Closing price time series', figsize=(10, 7));

Візуалізація значень часового ряду у розбитті по рокам

fig, axs = plt.subplots(nrows=data.year.nunique(), ncols=1, figsize=(10, 50))

for idx, year in enumerate(data.year.unique()):
    
    data_no_missing[data_no_missing.year == year].set_index('Date').Close.plot(
        title='Closing price time series for {}'.format(year), ax=axs[idx], rot='45');

Поквартальна візуалізація значень часового ряду

data_no_missing.set_index('Date_index').Close.resample('Q').mean().plot(
        title='Quarterely Closing price time series', rot='45');

fig, axs = plt.subplots(nrows=1, ncols=data.year.nunique(), figsize=(30, 10))

for idx, year in enumerate(data.year.unique()):
    
    data_no_missing[data_no_missing.year == year].set_index('Date_index').Close.resample('Q').mean().plot(
        title='Quarterely Closing price time series for {}'.format(year), ax=axs[idx], rot='45');

Помісячна візуалізація значень часового ряду

data_no_missing.set_index('Date_index').Close.resample('M').mean().plot(
        title='Quarterely Closing price time series', rot='45');

fig, axs = plt.subplots(nrows=1, ncols=data.year.nunique(), figsize=(30, 10))

for idx, year in enumerate(data.year.unique()):
    
    data_no_missing[data_no_missing.year == year].set_index('Date_index').Close.resample('M').mean().plot(
        title='Quarterely Closing price time series for {}'.format(year), ax=axs[idx], rot='45');

Наведені графіки свідчать про наявність так званого "mean-revesring" тренду

Перевірка на стаціонарність

Тест Дікі-Фулера

stationarity_test(data_no_missing.Close, smt.adfuller)

{'adfuller_statistics': -1.2810249204236723,
 'adfuller_p_value': 0.63780811113391,
 'adfuller_critical_values': {'1%': -3.4339382310452033,
  '5%': -2.863125003847544,
  '10%': -2.56761380228936}}

KPSS тест

stationarity_test(data_no_missing.Close, smt.kpss)

{'kpss_statistics': 5.98948825089506,
 'kpss_p_value': 0.01,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Бачимо, що вихідний часовий ряд не є стаціонарним

Декомпозиція часового ряду

data_no_missing.head(1)

	Date_index	Date	Open	High	Low	Close	Volume	year	quarter	month
0	2016-02-11	2016-02-11	29.33	29.51	29.030001	29.27	4805000.0	2016	1	2

data_no_missing = data_no_missing.set_index('Date_index')

Additive model

period=5

sesonal_decomposition_additive_5 = plot_decomposition(data_no_missing.Close, 'additive', 5)

Тест на стаціонарність для залишків

stationarity_test(sesonal_decomposition_additive_5.resid.dropna(), smt.adfuller)

{'adfuller_statistics': -15.8271072749015,
 'adfuller_p_value': 1.0043291380950998e-28,
 'adfuller_critical_values': {'1%': -3.4339840952648695,
  '5%': -2.8631452508003057,
  '10%': -2.567624583142913}}

stationarity_test(sesonal_decomposition_additive_5.resid.dropna(), smt.kpss)

{'kpss_statistics': 0.011048183295121446,
 'kpss_p_value': 0.1,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Additive model

period=20

sesonal_decomposition_additive_20 = plot_decomposition(data_no_missing.Close, 'additive', 20)

Тест на стаціонарність для залишків

stationarity_test(sesonal_decomposition_additive_20.resid.dropna(), smt.adfuller)

{'adfuller_statistics': -12.92787036050939,
 'adfuller_p_value': 3.754426786446961e-24,
 'adfuller_critical_values': {'1%': -3.434022876868246,
  '5%': -2.8631623708604996,
  '10%': -2.5676336990659903}}

stationarity_test(sesonal_decomposition_additive_20.resid.dropna(), smt.kpss)

{'kpss_statistics': 0.012725962247832222,
 'kpss_p_value': 0.1,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Additive model

period=253

sesonal_decomposition_additive_253 = plot_decomposition(data_no_missing.Close, 'additive', 253)

Тест на стаціонарність для залишків

stationarity_test(sesonal_decomposition_additive_253.resid.dropna(), smt.adfuller)

{'adfuller_statistics': -4.317859037108565,
 'adfuller_p_value': 0.000413621436312785,
 'adfuller_critical_values': {'1%': -3.4345140199818918,
  '5%': -2.8633791658322503,
  '10%': -2.567749139071643}}

stationarity_test(sesonal_decomposition_additive_253.resid.dropna(), smt.kpss)

{'kpss_statistics': 0.09266132310912872,
 'kpss_p_value': 0.1,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Multiplicative model

period=5

sesonal_decomposition_multiplicative_5 = plot_decomposition(data_no_missing.Close, 'multiplicative', 5)

Тест на стаціонарність для залишків

stationarity_test(sesonal_decomposition_multiplicative_5.resid.dropna(), smt.adfuller)

{'adfuller_statistics': -15.13311575225083,
 'adfuller_p_value': 7.1846792792620545e-28,
 'adfuller_critical_values': {'1%': -3.4339840952648695,
  '5%': -2.8631452508003057,
  '10%': -2.567624583142913}}

stationarity_test(sesonal_decomposition_multiplicative_5.resid.dropna(), smt.kpss)

{'kpss_statistics': 0.032780619982659895,
 'kpss_p_value': 0.1,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Multiplicative model

period=20

sesonal_decomposition_multiplicative_20 = plot_decomposition(data_no_missing.Close, 'multiplicative', 20)

Тест на стаціонарність для залишків

stationarity_test(sesonal_decomposition_multiplicative_20.resid.dropna(), smt.adfuller)

{'adfuller_statistics': -12.969482066859548,
 'adfuller_p_value': 3.1028460195163162e-24,
 'adfuller_critical_values': {'1%': -3.4340249409468155,
  '5%': -2.8631632820375903,
  '10%': -2.5676341842417187}}

stationarity_test(sesonal_decomposition_multiplicative_20.resid.dropna(), smt.kpss)

{'kpss_statistics': 0.029767313939175324,
 'kpss_p_value': 0.1,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Multiplicative model

period=253

sesonal_decomposition_multiplicative_253 = plot_decomposition(data_no_missing.Close, 'multiplicative', 253)

Тест на стаціонарність для залишків

stationarity_test(sesonal_decomposition_multiplicative_253.resid.dropna(), smt.adfuller)

{'adfuller_statistics': -4.185755600115316,
 'adfuller_p_value': 0.00069645297351933,
 'adfuller_critical_values': {'1%': -3.4345487774977768,
  '5%': -2.8633945067663817,
  '10%': -2.5677573081032214}}

stationarity_test(sesonal_decomposition_multiplicative_253.resid.dropna(), smt.kpss)

{'kpss_statistics': 0.09682880596583154,
 'kpss_p_value': 0.1,
 'kpss_critical_values': {'10%': 0.347,
  '5%': 0.463,
  '2.5%': 0.574,
  '1%': 0.739}}

Побудова моделей за допомогою крос-валідації для різних наборів порядків

data_no_missing = data_no_missing.reset_index(drop=False)

data_no_missing.head(2)

	Date_index	Date	Open	High	Low	Close	Volume	year	quarter	month
0	2016-02-11	2016-02-11	29.33	29.510000	29.030001	29.27	4805000.0	2016	1	2
1	2016-02-12	2016-02-12	29.52	29.950001	29.410000	29.90	3116500.0	2016	1	2

ORDERS_RANGE = range(1, 11)

N_SPLITS = 7

INDEX = pd.MultiIndex.from_product((ORDERS_RANGE, ORDERS_RANGE, list(range(N_SPLITS))))

def get_cross_val_results(data, n_splits, test_size, lags, orders_range=ORDERS_RANGE, plot=False):
    
    all_metrics_df_arma = pd.DataFrame()
    all_metrics_df_test_arma = pd.DataFrame()
    
    all_metrics_df_ar = pd.DataFrame()
    all_metrics_df_test_ar = pd.DataFrame()
    
    for p, q in tqdm(product(orders_range, orders_range)):
        
        metrics_df_arma, metrics_df_test_arma, metrics_df_ar, metrics_df_test_ar = make_cross_validation(
            data, n_splits=n_splits, test_size=test_size, lags=lags, ar_order=(p, 0), arma_order=(p, q),
            plot=plot)
        
        all_metrics_df_arma = pd.concat((all_metrics_df_arma, metrics_df_arma))
        all_metrics_df_test_arma = pd.concat((all_metrics_df_test_arma, metrics_df_test_arma))
        
        all_metrics_df_ar = pd.concat((all_metrics_df_ar, metrics_df_ar))
        all_metrics_df_test_ar = pd.concat((all_metrics_df_test_ar, metrics_df_test_ar))
        
    return all_metrics_df_arma, all_metrics_df_test_arma, all_metrics_df_ar, all_metrics_df_test_ar

all_metrics_df_arma, all_metrics_df_test_arma, all_metrics_df_ar, all_metrics_df_test_ar = get_cross_val_results(
    data_no_missing, N_SPLITS, 100, 30)

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IDX: 0, P: 9, Q: 9

90it [55:40, 24.88s/it]

IDX: 0, P: 9, Q: 10

92it [1:00:59, 91.19s/it]

IDX: 4, P: 10, Q: 2

93it [1:01:32, 73.81s/it]

IDX: 1, P: 10, Q: 3

94it [1:03:15, 82.64s/it]

IDX: 2, P: 10, Q: 4

95it [1:04:41, 83.65s/it]

IDX: 2, P: 10, Q: 5

96it [1:06:21, 88.35s/it]

IDX: 2, P: 10, Q: 6

97it [1:07:17, 78.77s/it]

IDX: 1, P: 10, Q: 7

98it [1:07:53, 65.77s/it]

IDX: 1, P: 10, Q: 8

99it [1:08:03, 49.02s/it]

IDX: 0, P: 10, Q: 9

100it [1:08:12, 40.93s/it]

IDX: 0, P: 10, Q: 10

all_metrics_df_arma.head()

	RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
(1, 1, 0)	0.355832	142.822990	0.126616	0.216802	0.008130	0.992750	2.042583	-2325.119615	-2310.035011
(1, 1, 1)	0.335239	126.770642	0.112385	0.205070	0.008160	0.994842	2.016626	-2459.607160	-2444.522556
(1, 1, 2)	0.326475	120.228901	0.106586	0.199987	0.008418	0.995336	1.968391	-2519.370913	-2504.286309
(1, 1, 3)	0.312534	110.180051	0.097677	0.190383	0.008254	0.995766	2.007580	-2617.824530	-2602.739926
(1, 1, 4)	0.370697	155.005605	0.137416	0.218120	0.010264	0.994934	2.002262	-2232.786892	-2217.702288

all_metrics_df_arma.to_csv('all_metrics_df.csv', index=True) all_metrics_df_test_arma.to_csv('all_metrics_df_test.csv', index=True) all_metrics_df_ar.to_csv('all_metrics_df_ar.csv', index=True) all_metrics_df_test_ar.to_csv('all_metrics_df_test_ar.csv', index=True)

idx = all_metrics_df_arma.index.tolist()
idx = [tuple(list(map(int, el.replace('(', '').replace(')', '').split(', ')))) for el in idx]
idx = pd.MultiIndex.from_tuples(idx, names=['P', 'Q', 'Fold Number'])

all_metrics_df_arma.index = idx

all_metrics_df_arma.head()

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	1	0	0.355832	142.822990	0.126616	0.216802	0.008130	0.992750	2.042583	-2325.119615	-2310.035011
		1	0.335239	126.770642	0.112385	0.205070	0.008160	0.994842	2.016626	-2459.607160	-2444.522556
		2	0.326475	120.228901	0.106586	0.199987	0.008418	0.995336	1.968391	-2519.370913	-2504.286309
		3	0.312534	110.180051	0.097677	0.190383	0.008254	0.995766	2.007580	-2617.824530	-2602.739926
		4	0.370697	155.005605	0.137416	0.218120	0.010264	0.994934	2.002262	-2232.786892	-2217.702288

idx = all_metrics_df_test_arma.index.tolist()
idx = [tuple(list(map(int, el.replace('(', '').replace(')', '').split(', ')))) for el in idx]
idx = pd.MultiIndex.from_tuples(idx, names=['P', 'Q', 'Fold Number'])

all_metrics_df_test_arma.index = idx

all_metrics_df_test_arma.head()

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	1	0	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	2.042583	-316.162481	-308.346970
		1	0.266160	7.084140	0.070841	0.142656	0.007994	0.961977	2.016626	-258.731167	-250.915657
		2	0.186904	3.493324	0.034933	0.120744	0.006046	0.906160	1.968391	-329.431633	-321.616122
		3	0.452306	20.458108	0.204581	0.299875	0.019375	0.976064	2.007580	-152.679090	-144.863579
		4	0.309901	9.603844	0.096038	0.195896	0.012715	0.928230	2.002262	-228.300679	-220.485168

idx = all_metrics_df_ar.index.tolist()
idx = [tuple(list(map(int, el.replace('(', '').replace(')', '').split(', ')))) for el in idx]
idx = pd.MultiIndex.from_tuples(idx, names=['P', 'Q', 'Fold Number'])

all_metrics_df_ar.index = idx

all_metrics_df_ar.head()

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	0	0	0.324809	119.005291	0.105501	0.216761	0.008144	0.993959	2.281557	-2532.909767	-2522.853364
		1	0.309103	107.774703	0.095545	0.205739	0.008190	0.995615	2.281591	-2644.722747	-2634.666344
		2	0.290934	95.476646	0.084642	0.194519	0.008195	0.996296	2.313043	-2781.392684	-2771.336281
		3	0.281592	89.443897	0.079294	0.186205	0.008072	0.996563	2.302493	-2855.017351	-2844.960948
		4	0.338974	129.610740	0.114903	0.217722	0.010253	0.995764	2.298073	-2436.615001	-2426.558598

idx = all_metrics_df_test_ar.index.tolist()
idx = [tuple(list(map(int, el.replace('(', '').replace(')', '').split(', ')))) for el in idx]
idx = pd.MultiIndex.from_tuples(idx, names=['P', 'Q', 'Fold Number'])

all_metrics_df_test_ar.index = idx

all_metrics_df_test_ar.head()

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	0	0	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	2.281557	-318.162481	-312.952140
		1	0.266160	7.084140	0.070841	0.142656	0.007994	0.961977	2.281591	-260.731167	-255.520827
		2	0.186904	3.493324	0.034933	0.120744	0.006046	0.906160	2.313043	-331.431633	-326.221292
		3	0.452306	20.458108	0.204581	0.299875	0.019375	0.976064	2.302493	-154.679090	-149.468749
		4	0.309901	9.603844	0.096038	0.195896	0.012715	0.928230	2.298073	-230.300679	-225.090338

all_metrics_df_arma.to_csv('all_metrics_df_arma.csv', index=True) all_metrics_df_test_arma.to_csv('all_metrics_df_test_arma.csv', index=True) all_metrics_df_ar.to_csv('all_metrics_df_ar.csv', index=True) all_metrics_df_test_ar.to_csv('all_metrics_df_test_ar.csv', index=True)

Розподіл метрик по порядкам моделей

ARMA

Тренувальні вибірки

fig, axs = plt.subplots(nrows=all_metrics_df_arma.shape[1], ncols=1, figsize=(15, 50))

for idx, metric_title in enumerate(all_metrics_df_arma.columns):
    all_metrics_df_arma.reset_index().groupby(['P', 'Q'])[metric_title].mean().plot(
        title='{} distribution through order of ARMA model'.format(metric_title), ax=axs[idx]);

Тестувальні вибірки

fig, axs = plt.subplots(nrows=all_metrics_df_test_arma.shape[1], ncols=1, figsize=(15, 50))

for idx, metric_title in enumerate(all_metrics_df_test_arma.columns):
    all_metrics_df_test_arma.reset_index().groupby(['P', 'Q'])[metric_title].mean().plot(
        title='{} distribution through order of ARMA model'.format(metric_title), ax=axs[idx]);

Побудова ACF та PACF для кожного з фолдів

(all_metrics_df_arma_selected, all_metrics_df_test_arma_selected, all_metrics_df_ar_selected,
 all_metrics_df_test_ar_selected) = make_cross_validation(data_no_missing, n_splits=N_SPLITS, test_size=100, 
                                                          lags=30, ar_order=(8, 0), arma_order=(8, 9), 
                                                          plot=True
                                                         )

<Figure size 720x576 with 0 Axes>

<Figure size 720x576 with 0 Axes>

IDX: 0, P: 8, Q: 9

Метрики у вигляді таблиць

ARMA

all_metrics_df_arma.shape, all_metrics_df_test_arma.shape

((439, 9), (439, 9))

all_metrics_df_arma.head(3)

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	1	0	0.355832	142.822990	0.126616	0.216802	0.008130	0.992750	2.042583	-2325.119615	-2310.035011
		1	0.335239	126.770642	0.112385	0.205070	0.008160	0.994842	2.016626	-2459.607160	-2444.522556
		2	0.326475	120.228901	0.106586	0.199987	0.008418	0.995336	1.968391	-2519.370913	-2504.286309

all_metrics_df_test_arma.head(3)

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	1	0	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	2.042583	-316.162481	-308.346970
		1	0.266160	7.084140	0.070841	0.142656	0.007994	0.961977	2.016626	-258.731167	-250.915657
		2	0.186904	3.493324	0.034933	0.120744	0.006046	0.906160	1.968391	-329.431633	-321.616122

усереднюємо метрики по фолдам для кожного набору порядків моделі

all_train_metrics_resampled_arma = all_metrics_df_arma.reset_index().groupby(
    ['P', 'Q']).mean().drop('Fold Number', axis=1)

all_test_metrics_resampled_arma = all_metrics_df_test_arma.reset_index().groupby(
    ['P', 'Q']).mean().drop('Fold Number', axis=1)

pd.set_option('display.max.rows', None)

all_train_metrics_resampled_arma.to_csv('all_train_metrics_df_resampled_arma.csv', index=True) all_test_metrics_resampled_arma.to_csv('all_test_metrics_df_resampled_arma.csv', index=True)

all_train_metrics_resampled_arma

		RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q
1	1	0.352968	141.343770	0.125305	0.211973	0.009462	0.994768	2.006301	-2349.923994	-2334.839390
	2	0.357808	145.047011	0.128588	0.214923	0.009588	0.994622	1.951906	-2315.616528	-2295.503722
	3	0.353528	141.803108	0.125712	0.212204	0.009469	0.994744	2.001595	-2342.469214	-2317.328207
	4	0.353523	141.789660	0.125700	0.212749	0.009495	0.994744	2.003550	-2340.416391	-2310.247182
	5	0.352548	140.988720	0.124990	0.212650	0.009487	0.994770	2.013442	-2344.497798	-2309.300388
	6	0.354381	142.500849	0.126331	0.214723	0.009587	0.994721	1.998220	-2331.133789	-2290.908178
2	1	0.353013	141.434825	0.125385	0.212198	0.009471	0.994760	2.010632	-2348.086747	-2327.973941
	2	0.352351	140.834518	0.124853	0.211686	0.009449	0.994788	2.018658	-2349.733037	-2324.592030
	3	0.361603	148.473660	0.131626	0.219063	0.009801	0.994503	1.918741	-2290.413016	-2260.243807
	4	0.356193	144.120737	0.127767	0.216370	0.009693	0.994679	1.987288	-2322.782067	-2287.584657
	5	0.356404	144.196850	0.127834	0.216278	0.009669	0.994666	1.983857	-2318.787404	-2278.561792
	6	0.354689	142.740865	0.126543	0.215949	0.009666	0.994713	2.006482	-2327.082468	-2281.828655
	7	0.354326	142.453741	0.126289	0.216070	0.009671	0.994724	2.015839	-2327.442513	-2277.160499
	8	0.355646	143.533979	0.127246	0.216334	0.009673	0.994688	1.997118	-2317.188487	-2261.878271
	9	0.354160	142.529696	0.126356	0.216368	0.009686	0.994730	2.021077	-2326.198828	-2265.860411
	10	0.350171	138.491226	0.122776	0.217135	0.008384	0.993618	2.000755	-2342.731369	-2277.364750
3	1	0.354129	142.314198	0.126165	0.213187	0.009515	0.994727	1.995204	-2338.861075	-2313.720068
	2	0.353943	142.162914	0.126031	0.213346	0.009523	0.994733	2.002729	-2338.035130	-2307.865921
	3	0.354940	142.970137	0.126747	0.215323	0.009643	0.994709	2.001808	-2329.701239	-2294.503829
	4	0.356296	143.786897	0.127471	0.215369	0.009605	0.994653	1.979990	-2316.887675	-2276.662064
	5	0.353771	141.989960	0.125878	0.214771	0.009589	0.994737	2.015637	-2332.852878	-2287.599065
	6	0.354120	142.310703	0.126162	0.214722	0.009591	0.994729	2.013913	-2328.939140	-2278.657125
	7	0.354626	142.835472	0.126627	0.215027	0.009610	0.994716	2.008847	-2324.649843	-2269.339627
	8	0.355132	143.114733	0.126875	0.215420	0.009628	0.994696	2.006820	-2318.433799	-2258.095382
	9	0.355916	143.778521	0.127463	0.216551	0.009680	0.994671	2.005769	-2311.715455	-2246.348837
	10	0.349166	137.653656	0.122033	0.216504	0.008362	0.993663	2.012614	-2346.861580	-2276.466760
4	1	0.354687	142.789044	0.126586	0.214170	0.009560	0.994711	1.996059	-2333.522254	-2303.353045
	2	0.353997	142.226916	0.126088	0.213219	0.009521	0.994732	2.000094	-2335.848402	-2300.650991
	3	0.354824	142.825845	0.126619	0.215808	0.009647	0.994702	2.005583	-2328.074988	-2287.849376
	4	0.354418	142.522183	0.126349	0.214591	0.009578	0.994717	2.004480	-2328.841875	-2283.588062
	5	0.358492	145.799750	0.129255	0.217886	0.009740	0.994606	1.960475	-2300.840482	-2250.558468
	6	0.355214	143.117383	0.126877	0.215587	0.009638	0.994697	1.995393	-2319.371855	-2264.061640
	7	0.345390	134.680028	0.119397	0.213735	0.008257	0.993802	2.029919	-2375.287276	-2314.948859
	8	0.348470	137.150744	0.121588	0.215685	0.008333	0.993679	2.009232	-2353.734917	-2288.368298
	9	0.349007	137.574960	0.121964	0.216094	0.008345	0.993660	2.007076	-2348.265437	-2277.870617
	10	0.350156	138.444191	0.122734	0.216736	0.008371	0.993625	1.998902	-2338.545362	-2263.122340
5	1	0.354260	142.398797	0.126240	0.214422	0.009571	0.994722	2.002256	-2333.854987	-2298.657577
	2	0.354879	142.943992	0.126723	0.215180	0.009609	0.994702	1.996783	-2328.325572	-2288.099960
	3	0.354265	142.373985	0.126218	0.215320	0.009625	0.994725	2.008142	-2329.585355	-2284.331543
	4	0.355658	143.567656	0.127276	0.214898	0.009602	0.994684	1.992287	-2319.309622	-2269.027607
	5	0.356087	143.917833	0.127587	0.216208	0.009676	0.994671	1.993551	-2314.598525	-2259.288309
	6	0.356876	144.345654	0.127966	0.216804	0.009682	0.994646	1.977778	-2305.925270	-2245.586853
	7	0.349967	138.309894	0.122615	0.216281	0.008351	0.993629	2.000557	-2343.882516	-2278.515898
	8	0.342017	132.152149	0.117156	0.212659	0.008455	0.994209	2.004674	-2394.177099	-2323.782279
	9	0.348429	137.140826	0.121579	0.216061	0.008344	0.993677	2.010902	-2350.188956	-2274.765934
	10	0.350798	138.975320	0.123205	0.217694	0.008406	0.993597	1.994096	-2332.604314	-2252.153091
6	1	0.354290	142.373329	0.126217	0.214200	0.009558	0.994720	2.002369	-2331.272639	-2291.047027
	2	0.354115	142.257266	0.126115	0.215019	0.009611	0.994731	2.008175	-2330.568115	-2285.314302
	3	0.355573	143.483021	0.127201	0.216342	0.009675	0.994682	1.998362	-2319.732055	-2269.450040
	4	0.353755	142.049086	0.125930	0.214104	0.009571	0.994743	2.018217	-2329.505369	-2274.195154
	5	0.349346	137.788423	0.122153	0.214867	0.008296	0.993658	1.994430	-2349.639580	-2289.301162
	6	0.348200	136.922482	0.121385	0.215133	0.008305	0.993692	2.007798	-2355.355784	-2289.989165
	7	0.361874	148.743328	0.131865	0.220492	0.009875	0.994514	1.930791	-2272.992699	-2202.597879
	8	0.340436	130.934670	0.116077	0.210883	0.008380	0.994262	2.011360	-2402.640081	-2327.217060
	9	0.341314	131.621346	0.116686	0.211631	0.008411	0.994230	2.005096	-2394.914508	-2314.463285
	10	0.350000	138.375633	0.122673	0.217047	0.008381	0.993620	1.999692	-2335.992581	-2250.513156
7	1	0.354457	142.551413	0.126375	0.214586	0.009579	0.994715	2.003651	-2328.571500	-2283.317688
	2	0.355188	143.131762	0.126890	0.215740	0.009648	0.994696	1.999052	-2321.828144	-2271.546130
	3	0.355334	143.272501	0.127015	0.216601	0.009692	0.994695	2.006024	-2319.101280	-2263.791064
	4	0.355758	143.658239	0.127357	0.216099	0.009668	0.994681	2.002292	-2314.754404	-2254.415987
	5	0.348987	137.547116	0.121939	0.215603	0.008328	0.993663	2.013102	-2350.294908	-2284.928289
	6	0.349047	137.586373	0.121974	0.215775	0.008334	0.993662	2.008138	-2347.849302	-2277.454482
	7	0.341809	132.044039	0.117060	0.211602	0.008407	0.994207	2.002365	-2393.998315	-2318.575293
	8	0.344482	134.035221	0.118826	0.213298	0.008477	0.994131	1.966897	-2373.740176	-2293.288953
	9	0.349519	137.946570	0.122293	0.216187	0.008348	0.993647	2.002305	-2338.702224	-2253.222799
	10	0.362573	148.285789	0.131459	0.224121	0.008413	0.992473	1.980729	-2252.779693	-2162.272067
8	1	0.355129	143.103249	0.126865	0.216985	0.009702	0.994693	1.991701	-2322.353973	-2272.071959
	2	0.356328	144.097292	0.127746	0.216596	0.009692	0.994668	1.994466	-2312.930946	-2257.620730
	3	0.355992	143.852819	0.127529	0.217256	0.009724	0.994673	2.001800	-2313.334306	-2252.995889
	4	0.350226	138.511670	0.122794	0.216596	0.008363	0.993620	1.997679	-2342.185579	-2276.818960
	5	0.349965	138.295867	0.122603	0.216491	0.008361	0.993631	2.001312	-2341.802937	-2271.408117
	6	0.349897	138.246938	0.122559	0.216027	0.008341	0.993633	1.999307	-2340.275300	-2264.852278
	7	0.358394	145.848947	0.129299	0.218742	0.009800	0.994609	1.987884	-2290.464492	-2210.013269
	8	0.349671	138.068569	0.122401	0.216863	0.008382	0.993641	2.003087	-2337.729707	-2252.250283
9	1	0.354459	142.480512	0.126313	0.215271	0.009614	0.994714	2.006298	-2323.978963	-2268.668747
	2	0.335387	127.248339	0.112809	0.206635	0.008385	0.994569	1.992554	-2443.831747	-2383.493330
	3	0.342345	132.451628	0.117422	0.212668	0.008447	0.994189	1.995915	-2394.397101	-2329.030482
	4	0.351398	139.453902	0.123629	0.218098	0.008421	0.993575	1.992895	-2332.770386	-2262.375566
	5	0.350507	138.713008	0.122973	0.218406	0.008432	0.993614	2.001973	-2336.217555	-2260.794534
	6	0.352157	140.014136	0.124126	0.219913	0.008496	0.993556	1.998280	-2323.547209	-2243.095986
	7	0.362141	147.932978	0.131146	0.224745	0.008433	0.992490	1.997040	-2257.466705	-2171.987281
	8	0.362274	148.041468	0.131242	0.224338	0.008419	0.992485	1.990771	-2254.639760	-2164.132134
10	1	0.356789	144.560558	0.128157	0.217587	0.009741	0.994651	2.004227	-2308.794992	-2248.456575
	2	0.334850	126.844256	0.112451	0.206729	0.008388	0.994587	2.003279	-2445.475557	-2380.108938
	3	0.364315	149.714588	0.132726	0.227558	0.008542	0.992400	1.980841	-2249.962948	-2179.568128
	4	0.351056	139.170561	0.123378	0.217125	0.008386	0.993589	1.984902	-2332.868798	-2257.445777
	5	0.349766	138.141722	0.122466	0.216884	0.008375	0.993638	2.007841	-2339.101939	-2258.650716
	6	0.351604	139.594894	0.123754	0.219209	0.008468	0.993572	1.996477	-2325.265317	-2239.785893
	7	0.362097	147.896706	0.131114	0.225962	0.008476	0.992492	2.015891	-2255.743314	-2165.235689
	8	0.361125	147.104041	0.130411	0.223139	0.008371	0.992533	1.997431	-2259.805181	-2164.269353

all_test_metrics_resampled_arma

		RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q
1	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.006301	-270.723526	-262.908015
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.951906	-268.723526	-258.302845
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.001595	-266.723526	-253.697675
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.003550	-264.723526	-249.092505
	5	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.013442	-262.723526	-244.487334
	6	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.998220	-260.723526	-239.882164
2	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.010632	-268.723526	-258.302845
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.018658	-266.723526	-253.697675
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.918741	-264.723526	-249.092505
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.987288	-262.723526	-244.487334
	5	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.983857	-260.723526	-239.882164
	6	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.006482	-258.723526	-235.276994
	7	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.015839	-256.723526	-230.671824
	8	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.997118	-254.723526	-226.066654
	9	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.021077	-252.723526	-221.461483
	10	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.000755	-267.446824	-233.579612
3	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.995204	-266.723526	-253.697675
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.002729	-264.723526	-249.092505
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.001808	-262.723526	-244.487334
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.979990	-260.723526	-239.882164
	5	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.015637	-258.723526	-235.276994
	6	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.013913	-256.723526	-230.671824
	7	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.008847	-254.723526	-226.066654
	8	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.006820	-252.723526	-221.461483
	9	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.005769	-250.723526	-216.856313
	10	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.012614	-265.446824	-228.974442
4	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.996059	-264.723526	-249.092505
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.000094	-262.723526	-244.487334
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.005583	-260.723526	-239.882164
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.004480	-258.723526	-235.276994
	5	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.960475	-256.723526	-230.671824
	6	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.995393	-254.723526	-226.066654
	7	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.029919	-269.446824	-238.184782
	8	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.009232	-267.446824	-233.579612
	9	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.007076	-265.446824	-228.974442
	10	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.998902	-263.446824	-224.369271
5	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.002256	-262.723526	-244.487334
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.996783	-260.723526	-239.882164
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.008142	-258.723526	-235.276994
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.992287	-256.723526	-230.671824
	5	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.993551	-254.723526	-226.066654
	6	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.977778	-252.723526	-221.461483
	7	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.000557	-267.446824	-233.579612
	8	0.217597	4.855495	0.048555	0.133192	0.007303	0.946615	2.004674	-279.441760	-242.969378
	9	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.010902	-263.446824	-224.369271
	10	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.994096	-261.446824	-219.764101
6	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.002369	-260.723526	-239.882164
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.008175	-258.723526	-235.276994
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.998362	-256.723526	-230.671824
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.018217	-254.723526	-226.066654
	5	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.994430	-269.446824	-238.184782
	6	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.007798	-267.446824	-233.579612
	7	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.930791	-248.723526	-212.251143
	8	0.217597	4.855495	0.048555	0.133192	0.007303	0.946615	2.011360	-277.441760	-238.364208
	9	0.217597	4.855495	0.048555	0.133192	0.007303	0.946615	2.005096	-275.441760	-233.759037
	10	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.999692	-259.446824	-215.158931
7	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.003651	-258.723526	-235.276994
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.999052	-256.723526	-230.671824
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.006024	-254.723526	-226.066654
	4	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.002292	-252.723526	-221.461483
	5	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.013102	-267.446824	-233.579612
	6	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.008138	-265.446824	-228.974442
	7	0.217597	4.855495	0.048555	0.133192	0.007303	0.946615	2.002365	-277.441760	-238.364208
	8	0.217597	4.855495	0.048555	0.133192	0.007303	0.946615	1.966897	-275.441760	-233.759037
	9	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.002305	-259.446824	-215.158931
	10	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	1.980729	-286.162481	-239.269417
8	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.991701	-256.723526	-230.671824
	2	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.994466	-254.723526	-226.066654
	3	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.001800	-252.723526	-221.461483
	4	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.997679	-267.446824	-233.579612
	5	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.001312	-265.446824	-228.974442
	6	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.999307	-263.446824	-224.369271
	7	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	1.987884	-244.723526	-203.040803
	8	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.003087	-259.446824	-215.158931
9	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.006298	-254.723526	-226.066654
	2	0.276274	8.756148	0.087561	0.174863	0.010321	0.953978	1.992554	-246.251093	-214.989050
	3	0.217597	4.855495	0.048555	0.133192	0.007303	0.946615	1.995915	-281.441760	-247.574548
	4	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.992895	-265.446824	-228.974442
	5	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.001973	-263.446824	-224.369271
	6	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.998280	-261.446824	-219.764101
	7	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	1.997040	-288.162481	-243.874588
	8	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	1.990771	-286.162481	-239.269417
10	1	0.263594	7.743024	0.077430	0.170583	0.010423	0.945731	2.004227	-252.723526	-221.461483
	2	0.276274	8.756148	0.087561	0.174863	0.010321	0.953978	2.003279	-244.251093	-210.383880
	3	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	1.980841	-294.162481	-257.690098
	4	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.984902	-263.446824	-224.369271
	5	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	2.007841	-261.446824	-219.764101
	6	0.232943	5.536580	0.055366	0.139415	0.007932	0.966843	1.996477	-259.446824	-215.158931
	7	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	2.015891	-286.162481	-239.269417
	8	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	1.997431	-284.162481	-234.664247

AR

all_metrics_df_ar.shape, all_metrics_df_test_ar.shape

((488, 9), (488, 9))

all_metrics_df_ar.head(3)

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	0	0	0.324809	119.005291	0.105501	0.216761	0.008144	0.993959	2.281557	-2532.909767	-2522.853364
		1	0.309103	107.774703	0.095545	0.205739	0.008190	0.995615	2.281591	-2644.722747	-2634.666344
		2	0.290934	95.476646	0.084642	0.194519	0.008195	0.996296	2.313043	-2781.392684	-2771.336281

all_metrics_df_test_ar.head(3)

			RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q	Fold Number
1	0	0	0.199725	3.989019	0.039890	0.136175	0.007870	0.971710	2.281557	-318.162481	-312.952140
		1	0.266160	7.084140	0.070841	0.142656	0.007994	0.961977	2.281591	-260.731167	-255.520827
		2	0.186904	3.493324	0.034933	0.120744	0.006046	0.906160	2.313043	-331.431633	-326.221292

усереднюємо метрики по фолдам для кожного набору порядків моделі

all_train_metrics_resampled_ar = all_metrics_df_ar.reset_index().groupby(
    ['P', 'Q']).mean().drop('Fold Number', axis=1)

all_test_metrics_resampled_ar = all_metrics_df_test_ar.reset_index().groupby(
    ['P', 'Q']).mean().drop('Fold Number', axis=1)

all_train_metrics_resampled_ar.to_csv('all_train_metrics_df_resampled_ar.csv', index=True) all_test_metrics_resampled_ar.to_csv('all_test_metrics_df_resampled_ar.csv', index=True)

all_train_metrics_resampled_ar

		RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q
1	0	0.320788	116.736332	0.103490	0.210980	0.009295	0.995534	2.296687	-2567.569871	-2557.513468
2	0	0.331748	124.801750	0.110640	0.219617	0.009774	0.995342	2.136496	-2489.261670	-2474.177066
3	0	0.336223	128.319315	0.113758	0.221751	0.009894	0.995224	2.070553	-2458.133204	-2438.020398
4	0	0.335666	127.807130	0.113304	0.220947	0.009662	0.995096	2.057074	-2459.026577	-2433.885570
5	0	0.338357	129.764005	0.115039	0.220173	0.009618	0.995016	2.038574	-2438.133510	-2407.964301
6	0	0.337719	129.278780	0.114609	0.217860	0.009436	0.994973	2.022952	-2440.402009	-2405.204599
7	0	0.337805	129.291979	0.114621	0.217273	0.009324	0.994890	2.031450	-2437.369662	-2397.144051
8	0	0.343651	133.877056	0.118685	0.220627	0.009509	0.994715	2.016924	-2397.297641	-2352.043828
9	0	0.339853	130.745184	0.115909	0.219518	0.009023	0.994472	2.011099	-2418.747721	-2368.465707
10	0	0.341482	131.964875	0.116990	0.220127	0.009026	0.994391	2.009170	-2405.656164	-2350.345948

all_test_metrics_resampled_ar

		RMSE	RSS	MSE	MAE	MAPE	R2	durbin_watson	aic	bic
P	Q
1	0	0.258040	7.416589	0.074166	0.167591	0.010201	0.947990	2.296687	-276.674739	-271.464399
2	0	0.261503	7.611773	0.076118	0.168884	0.010282	0.945771	2.136496	-272.119809	-264.304298
3	0	0.261503	7.611773	0.076118	0.168884	0.010282	0.945771	2.070553	-270.119809	-259.699128
4	0	0.253372	7.101351	0.071014	0.162274	0.009730	0.945928	2.057074	-273.549800	-260.523949
5	0	0.256989	7.344201	0.073442	0.164776	0.009905	0.946475	2.038574	-269.279423	-253.648402
6	0	0.257584	7.399125	0.073991	0.164770	0.009868	0.947153	2.022952	-267.044384	-248.808193
7	0	0.255640	7.268648	0.072686	0.162825	0.009702	0.948202	2.031450	-266.215680	-245.374318
8	0	0.247410	6.739253	0.067393	0.158262	0.009410	0.947221	2.016924	-269.663924	-246.217392
9	0	0.246930	6.699290	0.066993	0.155407	0.009079	0.951952	2.011099	-267.692329	-241.640627
10	0	0.241918	6.335399	0.063354	0.151621	0.008828	0.952699	2.009170	-268.494879	-239.838007